Unsupervised domain adaptation (DA) aims to perform classification tasks on the target domain by leveraging rich labeled data in the existing source domain. The key insight of DA is to reduce domain divergence by learning domain-invariant features or transferable instances. Despite its rapid development, there still exist several challenges to explore. At the feature level, aligning both domains only in a single way (i.e., geometrical or statistical) has limited ability to reduce the domain divergence. At the instance level, interfering instances often obstruct learning a discriminant subspace when performing the geometrical alignment. At the classifier level, only minimizing the empirical risk on the source domain may result in a negative transfer. To tackle these challenges, this article proposes a novel DA method, called discriminant geometrical and statistical alignment (DGSA). DGSA first aligns the geometrical structure of both domains by projecting original space into a Grassmann manifold, then matches the statistical distributions of both domains by minimizing their maximum mean discrepancy on the manifold. In the former step, DGSA only selects the density peaks to learn the Grassmann manifold and so to reduce the influences of interfering instances. In addition, DGSA exploits the high-confidence soft labels of target landmarks to learn a more discriminant manifold. In the latter step, a structural risk minimization (SRM) classifier is learned to match the distributions (both marginal and conditional) and predict the target labels at the same time. Extensive experiments on objection recognition and human activity recognition tasks demonstrate that DGSA can achieve better performance than the comparison methods.

中文翻译：

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判别几何和统计对齐与密度峰值的域适应


无监督域适应（DA）旨在通过利用现有源域中丰富的标记数据在目标域上执行分类任务。 DA 的关键见解是通过学习领域不变特征或可转移实例来减少领域分歧。尽管发展迅速，但仍然存在一些挑战需要探索。在特征级别，仅以单一方式（即几何或统计）对齐两个域减少域发散的能力有限。在实例级别，在执行几何对齐时，干扰实例通常会阻碍学习判别子空间。在分类器级别，仅最小化源域的经验风险可能会导致负迁移。为了应对这些挑战，本文提出了一种新颖的 DA 方法，称为判别几何和统计对齐（DGSA）。 DGSA 首先通过将原始空间投影到格拉斯曼流形中来对齐两个域的几何结构，然后通过最小化流形上的最大平均差异来匹配两个域的统计分布。在前一步中，DGSA仅选择密度峰值来学习格拉斯曼流形，从而减少干扰实例的影响。此外，DGSA 利用目标地标的高置信度软标签来学习更具判别力的流形。在后一步中，学习结构风险最小化（SRM）分类器来匹配分布（边际分布和条件分布）并同时预测目标标签。在物体识别和人类活动识别任务上的大量实验表明，DGSA 可以取得比比较方法更好的性能。